A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces
Functional Analysis
2022-07-07 v1
Abstract
We study a characterization of BV and Sobolev functions via nonlocal functionals in metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. Compared with previous works, we consider more general functionals. We also give a counterexample in the case demonstrating that unlike in Euclidean spaces, in metric measure spaces the limit of the nonlocal functions is only comparable, not necessarily equal, to the variation measure .
Keywords
Cite
@article{arxiv.2207.02488,
title = {A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces},
author = {Panu Lahti and Andrea Pinamonti and Xiaodan Zhou},
journal= {arXiv preprint arXiv:2207.02488},
year = {2022}
}